Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth. A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s. a. Substitute the values into the vertical motion formula h= -16t^2 +vt +c . Let h = 0. b. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.

Answer 1

Here the vertical motion formula is h = -16t^2 + 116t + 101 (feet)

How long will it take for the rocket to rise, stop rising, start falling and then his the ground? To find this, set h = 0 and solve for t. Omit negative results, if any.

-16t^2 + 116t + 101 = 0.

Since the solutions are unlikely to be "nice" numbers (integers), let's use the quadratic formula to solve this equation for t:

-116 plus or minus sqrt(116^2 - 4(-16)(101) )
t = ----------------------------------------------------------------
2(-16)
-116 plus or minus sqrt(19920)
= ---------------------------------------------
-32
-116 plus or minus 141.1
= -----------------------------------
-32

= -25.1/(-32) (discard) and t = -116 - 141.1
------------------
-32

t = 8.03.

The rocket will hit the ground 8.03 seconds after it is launched.